5,649 research outputs found

    Faster Worst Case Deterministic Dynamic Connectivity

    Get PDF
    We present a deterministic dynamic connectivity data structure for undirected graphs with worst case update time O(n(loglogn)2logn)O\left(\sqrt{\frac{n(\log\log n)^2}{\log n}}\right) and constant query time. This improves on the previous best deterministic worst case algorithm of Frederickson (STOC 1983) and Eppstein Galil, Italiano, and Nissenzweig (J. ACM 1997), which had update time O(n)O(\sqrt{n}). All other algorithms for dynamic connectivity are either randomized (Monte Carlo) or have only amortized performance guarantees

    Optimal decremental connectivity in planar graphs

    Get PDF
    We show an algorithm for dynamic maintenance of connectivity information in an undirected planar graph subject to edge deletions. Our algorithm may answer connectivity queries of the form `Are vertices uu and vv connected with a path?' in constant time. The queries can be intermixed with any sequence of edge deletions, and the algorithm handles all updates in O(n)O(n) time. This results improves over previously known O(nlogn)O(n \log n) time algorithm
    corecore